Composite substrate for electro-optic element and method for manufacturing the same

ABSTRACT

A composite substrate for an electro-optic element is disclosed. The composite substrate includes: an electro-optic crystal substrate having an electro-optic effect; a low-refractive-index layer being in contact with the electro-optic crystal substrate and having a lower refractive index than the electro-optical crystal substrate; and a support substrate bonded to the low-refractive-index layer at least via a bonding layer. A plurality of interfaces located between the low-refractive-index layer and the support substrate includes at least one rough interface having a roughness that is larger than a roughness of an interface between the electro-optic crystal substrate and the low-refractive-index layer.

CROSS-REFERENCE TO RELATED APPLICATION

This is a continuation of PCT/JP2019/027570 filed on Jul. 11, 2019,which claims priority to PCT/JP2018/041548 filed on Nov. 8, 2018, theentire contents of which are hereby incorporated by reference.

TECHNICAL FIELD

The art disclosed herein relates to a composite substrate for anelectro-optic element (such as an optical modulator) that uses anelectro-optic effect.

BACKGROUND

An electro-optic element such as an optical modulator is known. Theelectro-optic element can convert an electric signal to an opticalsignal by using an electro-optic effect. Such an electro-optic elementis essential in radio-over-fiber communication, and development thereofis in progress to realize fast and large-capacity communication.

Japanese Patent Application Publication No. 2010-85789 describes anoptical modulator. This optical modulator is one type of electro-opticelement, and is configured by using a composite substrate. The compositesubstrate includes an electro-optic crystal substrate and a supportsubstrate bonded to the electro-optic crystal substrate via a bondinglayer. Materials having a lower refractive index than the electro-opticcrystal substrate are employed in the support substrate and the bondinglayer.

SUMMARY

In conventional electro-optic elements including the aforementionedoptical modulator, the greater a thickness of a support substrate is,the higher a mechanical strength of a composite substrate (that is, amechanical strength of the electro-optic element) can be. On the otherhand, the larger the thickness of the support substrate becomes, themore likely it is that electromagnetic waves resonate within thecomposite substrate upon use of the electro-optic element in a radiofrequency band (for example, 10 GHz or higher) becomes higher. When sucha resonance occurs, a normal operation of the electro-optic element isthereby obstructed, such as by an unintended ripple (fluctuation)occurring in an output signal of the electro-optic element.

Due to this, in the disclosure herein, art that can reduce a resonanceof electromagnetic waves in a composite substrate is provided.

Solution to Technical Problem

When a high-frequency electric signal is applied to an electro-opticcrystal substrate, electromagnetic waves thereby generated propagateiteratively within a composite substrate in a thickness direction whilebeing reflected on surfaces and interfaces of the composite substrate.Further, when such electromagnetic waves overlap each other in the samephase, a resonance in the composite substrate as aforementioned occurs.Due to this, in the art disclosed herein, at least one of a plurality ofinterfaces present within a composite substrate is configured as a roughinterface having a large roughness. According to such a configuration,electromagnetic waves propagating within the composite substrate in athickness direction are refracted or reflected in various ways on therough interface, which creates numerous variations in paths along whichthe electromagnetic waves propagate. Due to this, the electromagneticwaves propagating within the composite substrate can be suppressed fromoverlapping each other in the same phase in the thickness direction.

A position where the rough interface is located is not particularlylimited. However, when the rough interface is an interface that is incontact with an electro-optic crystal substrate, light propagating inthe electro-optic crystal substrate could be diffused or absorbed by therough interface. To address this, the art disclosed herein includes alow-refractive-index layer that is in contact with the electro-opticcrystal substrate, and an interface between the electro-optic crystalsubstrate and the low-refractive-index layer is configured as a smoothinterface. According to this, diffusion and absorption of the lightpropagating in the electro-optic crystal substrate can be reduced, andthe light can be enclosed within the electro-optic crystal substrate.Further, as for the rough interface, the resonance of theelectromagnetic waves as aforementioned can be reduced by providing therough interface between the low-refractive-index layer and a supportsubstrate.

In one aspect of the present teachings, a composite substrate for anelectro-optic element is disclosed. The composite substrate maycomprise: an electro-optic crystal substrate having an electro-opticeffect; a low-refractive-index layer being in contact with theelectro-optic crystal substrate and having a lower refractive index thanthe electro-optical crystal substrate; and a support substrate bonded tothe low-refractive-index layer at least via a bonding layer. A pluralityof interfaces located between the low-refractive-index layer and thesupport substrate may include at least one rough interface having aroughness that is larger than a roughness of an interface between theelectro-optic crystal substrate and the low-refractive-index layer.

According to the aforementioned configuration, resonance of theelectromagnetic waves within the composite substrate can be reduced bypresence of the at least one rough interface in the composite substrate.On the other hand, since the interface between the electro-optic crystalsubstrate and the low-refractive-index layer is relatively smooth,diffusion and absorption of light propagating through the electro-opticcrystal substrate can be reduced, and the light can be enclosed withinthe electro-optic crystal substrate.

In another aspect of the present teachings, a method of manufacturing acomposite substrate for an electro-optic element is further disclosed.The method may comprise: forming a low-refractive-index layer on asurface of an electro-optic crystal substrate having an electro-opticeffect, the low-refractive-index layer having a lower refractive indexthan the electro-optic crystal substrate; forming a bonding layer on asurface of the low-refractive-index layer formed on the electro-opticcrystal substrate; and bonding a support substrate on a surface of thebonding layer formed on the low-refractive-index layer. A roughness ofthe surface of the low-refractive-index layer before the forming of thebonding layer may be larger than a roughness of the surface of theelectro-optic crystal substrate before the forming of thelow-refractive-index layer.

According to the aforementioned manufacturing method, the compositesubstrate that comprises the electro-optic crystal substrate, thelow-refractive-index layer being in contact with the electro-opticcrystal substrate, and the support substrate bonded to thelow-refractive-index layer at least via the bonding layer can bemanufactured. Especially with this manufacturing method, the roughnessof the surface of the low-refractive-index layer before forming thebonding layer is larger than the roughness of the surface of theelectro-optic crystal substrate before forming the low-refractive-indexlayer. As such, in the manufactured composite substrate, the interfacebetween the low-refractive-index layer and the bonding layer can beconfigured as an interface having a larger roughness than the interfacebetween the electro-optic crystal substrate and the low-refractive-indexlayer.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a perspective view schematically showing a composite substrate10 of a first embodiment.

FIG. 2 schematically shows a cross-sectional structure of the compositesubstrate 10 of the first embodiment.

FIG. 3 shows a step of a method of manufacturing the composite substrate10 of the first embodiment.

FIG. 4 shows a step of the method of manufacturing the compositesubstrate 10 of the first embodiment.

FIG. 5 shows a step of the method of manufacturing the compositesubstrate 10 of the first embodiment.

FIG. 6 shows a step of the method of manufacturing the compositesubstrate 10 of the first embodiment.

FIG. 7 shows a step of the method of manufacturing the compositesubstrate 10 of the first embodiment.

FIG. 8 shows a variant of the composite substrate 10, in whichelectrodes 32, 34 configured to apply electric signals to anelectro-optic crystal substrate 12 and an optical waveguide region 36disposed in the electro-optic crystal substrate 12 are added.

FIG. 9 shows a variant of the composite substrate 10, in which a ridgeportion 13 is formed on an upper surface 12 a of the electro-opticcrystal substrate 12.

FIG. 10 shows a variant of the composite substrate 10, in whichelectrodes 42, 44 configured to apply electric signals to the ridgeportion 13 are added. In this variant, a c-axis of the electro-opticcrystal substrate 12 is parallel to the electro-optic crystal substrate12.

FIG. 11 shows a variant of the composite substrate 10, in whichelectrodes 52, 54 configured to apply electric signals to the ridgeportion 13 are added. In this variant, the c-axis of the electro-opticcrystal substrate 12 is perpendicular to the electro-optic crystalsubstrate 12.

FIG. 12 schematically shows a cross-sectional structure of a compositesubstrate 10 a of a second embodiment.

FIG. 13 is a diagram explaining a method of manufacturing the compositesubstrate 10 a of the second embodiment.

FIG. 14 schematically shows a cross-sectional structure of a compositesubstrate 10 b of a third embodiment.

FIG. 15 is a diagram explaining a method of manufacturing the compositesubstrate 10 b of the third embodiment.

FIG. 16 schematically shows a cross-sectional structure of a compositesubstrate 10 c of a fourth embodiment.

FIG. 17 is a diagram explaining a method of manufacturing the compositesubstrate 10 c of the fourth embodiment.

DETAILED DESCRIPTION

In an aspect of the art disclosed herein, an arithmetic roughnessaverage (Ra) of at least one rough interface having a large roughnessmay be in a range from 0.5 nm to 10 nm by giving consideration towavelengths of electromagnetic waves to be refracted or reflected on theinterface(s). According to such a configuration, the electromagneticwaves caused by electric signals applied to an electro-optic crystalsubstrate can effectively be refracted or reflected on the interface(s),and a resonance of the electromagnetic waves in a composite substratecan thereby be reduced.

Here, the arithmetic roughness average (Ra) is defined by JIS B 0031 andJIS B 0601, and a calculation procedure thereof is as follows. Firstly,a profile is extracted over a reference length 1 in a mean linedirection from a roughness curve. Next, an X-axis is defined in the meanline direction and a Y-axis is defined in a longitudinal magnificationdirection for this extracted portion, and a roughness curve thereof isexpressed by an equation y=f(x). Then, the arithmetic roughness average(Ra) is calculated by integrating absolute values of deviations of f(x)over the reference length 1 and dividing those integrated values by thereference length 1. A maximum height (Ry) is also well known as an indexrepresenting roughness, and in general, the maximum height (Ry) is saidto be around five to ten times the arithmetic roughness average (Ra).Based on this relationship, a maximum height (Ry) of the at least onerough interface may be in a range from 2.5 nm to 100 nm.

In an aspect of the art disclosed herein, a thickness of alow-refractive-index layer may be in a range from 0.1 μm to 10 μm. Alower limit of the thickness of the low-refractive-index layer may be atleast 0.65 μm, for example from a viewpoint of improving performance ofthe electro-optic element, and may further be at least 0.7 μm. Further,for example from a viewpoint of reducing the resonance of theelectromagnetic waves in the composite substrate by increasing theroughness of the at least one rough interface, the lower limit may morepreferably be at least 1.5 μm, and yet more preferably be at least 3 μm.On the other hand, for example from a viewpoint of reducing thermalstress that may be created in the composite substrate, an upper limit ofthe thickness of the low-refractive-index layer may be 9 μm at most, andfurther be 7 μm at most.

In an aspect of the art disclosed herein, a thickness of theelectro-optic crystal substrate may be in a range from 0.1 μm to 10 μm.A lower limit of the thickness of the electro-optic crystal substratemay be at least 0.3 μm, for example from a viewpoint of reducing lightpropagation loss, and preferably be at least 0.45 μm. On the other hand,for example from a viewpoint of improving performance of theelectro-optic element, an upper limit of the thickness of theelectro-optic crystal substrate may be 5 μm at most, and further be 2.8μm at most.

In an aspect of the art disclosed herein, the roughness of the at leastone rough interface may be at least three times a roughness of aninterface between the electro-optic crystal substrate and thelow-refractive-index layer, or may be at least five times as large, orten times as large. The lager a difference in the roughness of these twointerfaces is, the greater an effect of the art disclosed herein can be.

In an aspect of the art disclosed herein, an arithmetic roughnessaverage (Ra) of the interface between the electro-optic crystalsubstrate and the low-refractive-index layer may be in a range from 0.03nm (nanometers) to 0.5 nm, and the arithmetic roughness average (Ra) ofthe at least one rough interface may be in a range from 0.5 nm to 500nm. When the composite substrate satisfies these numerical requirements,the composite substrate achieving the effect of the art disclosed hereincan be manufactured with a relatively simple procedure.

In an aspect of the art disclosed herein, the at least one roughinterface may be an interface between the low-refractive-index layer anda bonding layer. In this case, an arithmetic roughness average (Ra) ofthe interface between the low-refractive-index layer and the bondinglayer may be at least one thousandth ( 1/1000) of the thickness of thelow-refractive-index layer. In addition thereto or as an alternativethereof, the arithmetic roughness average (Ra) of the interface betweenthe low-refractive-index layer and the bonding layer may be at least 0.5nm, and the thickness of the low-refractive-index layer may be at least0.5 μm (micrometers). When the composite substrate satisfies thesenumerical requirements, the composite substrate achieving the effect ofthe art disclosed herein can be manufactured with a relatively simpleprocedure.

In addition to or as an alternative to the above, the at least one roughinterface may be an interface between the bonding layer and a supportsubstrate. With such a configuration as well, the resonance of theelectromagnetic waves within the composite substrate can be reduced bypresence of the at least one rough interface in the composite substrate.

In addition to or as an alternative to the above, the compositesubstrate may further comprise an intermediate layer located between thelow-refractive-index layer and the bonding layer. In this case, the atleast one rough interface may be an interface between the intermediatelayer and the bonding layer. With such a configuration as well, theresonance of the electromagnetic waves within the composite substratecan be reduced by the presence of the at least one rough interface inthe composite substrate. A material constituting the intermediate layermay be a material which may be employed in the low-refractive-indexlayer or in the bonding layer, and further may be a material differentfrom material(s) actually employed in the low-refractive-index layer andthe bonding layer.

In addition to or as an alternative to the above, the compositesubstrate may further comprise an intermediate layer located between thebonding layer and the support layer. In this case, the at least onerough interface may be an interface between the intermediate layer andthe support layer. With such a configuration as well, the resonance ofthe electromagnetic waves within the composite substrate can be reducedby the presence of the at least one rough interface in the compositesubstrate.

In an aspect of the art disclosed herein, the composite substrate mayfurther comprise a conductive layer constituted of an electricconductor. In this case, the at least one rough interface may includeone or more interfaces located between the electro-optic crystalsubstrate and the conductive layer. When the conductive layer is presentinside the composite substrate, the electromagnetic waves propagatingthrough the composite substrate is intercepted without passing throughthe conductive layer, thus the electromagnetic waves propagate primarilybetween the electro-optic crystal substrate 12 and the conductive layer.Due to this, the at least one rough interface may be located between theelectro-optic crystal substrate and the conductive layer where theelectromagnetic waves primarily propagate.

In an aspect of the art disclosed herein, the conductive layer may be atleast a part of either the bonding layer or the intermediate layer. Inother words, when the bonding layer and/or the intermediate layer arenot located between the electro-optic crystal substrate 12 and the atleast one rough interface, a part of or all of the bonding layer and/orthe intermediate layer may be constituted of an electric conductor suchas metal.

In an aspect of the art disclosed herein, the electro-optic crystalsubstrate may be a substrate of lithium niobate (LiNbO₃: LN), lithiumtantalate (LiTaO₃: LT), potassium titanyl phosphate (KTiOPO₄: KIP),potassium lithium niobate (K_(x)Li_((1-x))NbO₂: KLN), potassium niobate(KNbO₃: KN), potassium tantalate niobate (KNb_(x)Ta_((1-x))O₃: KIN), ora solid solution of lithium niobate and lithium tantalate.

In an aspect of the art disclosed herein, the low-refractive-index layermay be constituted of at least one substance selected from a groupconsisting of silicon oxide (SiO₂), tantalum oxide (Ta₂O₅), aluminumoxide (Al₂O₃), magnesium fluoride (MgF₂), and calcium fluoride (CaF₂).

In an aspect of the art disclosed herein, the bonding layer may beconstituted of at least one substance selected from a group consistingof tantalum oxide (Ta₂O₅), niobium oxide (Nb₂O₅), silicon (Si), aluminumoxide (Al₂O₃), titanium oxide (TiO₂), gold (Au), silver (Ag), copper(Cu), aluminum (Al), platinum (Pt), and an alloy containing at least twoof the aforementioned metal elements.

In an aspect of the art disclosed herein, the support substrate may be asubstrate constituted of lithium niobate (LiNbO₃: LN), lithium tantalate(LiTaO₃: LT), silicon (Si), glass, sialon (Si₃N₄—Al₂O₃), mullite(3Al₂O₃.2SiO₂, 2Al₂O₃.SiO₂), aluminum nitride (AlN), silicon nitride(Si₃N₄), magnesium oxide (MgO), sapphire, quartz, crystal, galliumnitride (GaN), silicon carbide (SiC), or gallium oxide (Ga₂O₃). From aviewpoint of reducing resonance of the electromagnetic waves, thesupport substrate may have conductivity or semiconductivity. Forexample, lithium niobate and lithium tantalate are insulative materialsin their normal state, however, they can obtain conductivity in anoxygen deficient state. So-called black-LN and black-LT are examples ofsuch materials, and a black-LN or a black-LT substrate may be employedas the support substrate.

As aforementioned, the art disclosed herein may be embodied as a methodof manufacturing a composite substrate. In this manufacturing method, abonding layer is formed on a surface of a low-refractive-index layerhaving a large roughness. Thus, as for a surface of the bonding layer aswell, a roughness thereof may become relatively large. However, when asupport substrate is to be bonded to the surface of the bonding layer,the surface of the bonding layer is preferably smooth. Due to this, inan aspect of the art disclosed herein, the manufacturing method mayfurther comprise smoothing the surface of the bonding layer between theforming of the bonding layer and the bonding of the support substrate.According to such a configuration, an electro-optic crystal substrateand the support substrate can be well bonded.

In an aspect of the art disclosed herein, the forming of thelow-refractive-index layer may comprise forming the low-refractive-indexlayer by sputter deposition. When the low-refractive-index layer isformed by the sputter deposition, the roughness of the surface of thelow-refractive-index layer naturally becomes large. Due to this, byforming the low-refractive-index layer by sputter deposition, thelow-refractive-index layer having the surface with the large roughnesscan easily be formed. In the forming of the low-refractive-index layerby the sputter deposition, the greater a thickness of thelow-refractive-index layer is, the larger the roughness of the surfaceof the low-refractive-index layer becomes. Further, in the forming ofthe low-refractive-index layer, a process of roughening the surface ofthe low-refractive-index layer (such as lapping, sand blast, andetching) may be performed as needed.

In an aspect of the art disclosed herein, the manufacturing method mayfurther comprise forming the bonding layer on the surface of the supportsubstrate before the bonding of the support substrate. In this case, thebonding layer to be formed on the support substrate may be constitutedof the same material as the bonding layer formed on thelow-refractive-index layer, but not particularly limited thereto.According to such a configuration, the electro-optic crystal substrateand the support substrate can be well bonded.

Representative, non-limiting examples of the present disclosure will nowbe described in further detail with reference to the attached drawings.This detailed description is merely intended to teach a person of skillin the art further details for practicing aspects of the presentteachings and is not intended to limit the scope of the presentdisclosure. Furthermore, each of the additional features and teachingsdisclosed below may be utilized separately or in conjunction with otherfeatures and teachings to provide improved composite substrates, as wellas methods for using and manufacturing the same.

Moreover, combinations of features and steps disclosed in the followingdetailed description may not be necessary to practice the presentdisclosure in the broadest sense, and are instead taught merely toparticularly describe representative examples of the present disclosure.Furthermore, various features of the above-described and below-describedrepresentative examples, as well as the various independent anddependent claims, may be combined in ways that are not specifically andexplicitly enumerated in order to provide additional useful embodimentsof the present teachings.

All features disclosed in the description and/or the claims are intendedto be disclosed separately and independently from each other for thepurpose of original written disclosure, as well as for the purpose ofrestricting the claimed subject matter, independent of the compositionsof the features in the embodiments and/or the claims. In addition, allvalue ranges or indications of groups of entities are intended todisclose every possible intermediate value or intermediate entity forthe purpose of original written disclosure, as well as for the purposeof restricting the claimed subject matter.

Embodiments

(First Embodiment) A composite substrate 10 of a first embodiment and amanufacturing method thereof will be described with reference to thedrawings. The composite substrate 10 of the present embodiment may beemployed in various electro-optic elements such as an optical modulator.As shown in FIG. 1, the composite substrate 10 of the present embodimentis manufactured in a form of so-called a wafer, and is supplied to amanufacturer of the electro-optic element. Although this is merely anexample, a diameter of the composite substrate 10 may be about 10centimeters (4 inches). Normally, a plurality of electro-optic elementsis manufactured from one composite substrate 10. The composite substrate10 is not limited to the form of a wafer, and may be manufactured andsupplied in various forms.

As shown in FIGS. 1 and 2, the composite substrate 10 includes anelectro-optic crystal substrate 12, a low-refractive-index layer 14, abonding layer 16, and a support substrate 18. The electro-optic crystalsubstrate 12 is bonded to the support substrate 18 via thelow-refractive-index layer 14 and the bonding layer 16. These substrates12, 18 and layers 14, 16 spread parallel to each other over an entiretyof the composite substrate 10.

The electro-optic crystal substrate 12 is a topmost layer of thecomposite substrate 10, and an upper surface 12 a thereof is exposed tooutside. A part of or all of the electro-optic crystal substrate 12serves as an optical waveguide which transmits a light in each ofelectro-optic elements manufactured from the composite substrate 10. Theelectro-optic crystal substrate 12 is constituted of a crystal of amaterial having an electro-optic effect. As such, when an electric fieldis applied to the electro-optic crystal substrate 12, a refractive indexof the electro-optic crystal substrate 12 thereby changes. Especiallywhen the electric field is applied along a c-axis of the electro-opticcrystal substrate 12, the refractive index of the electro-optic crystalsubstrate 12 changes significantly.

Here, the c-axis of the electro-optic crystal substrate 12 may beparallel to the electro-optic crystal substrate 12. That is, theelectro-optic crystal substrate 12 may for example be a substrate of ax-cut or a y-cut. Alternatively, the c-axis of the electro-optic crystalsubstrate 12 may be perpendicular to the electro-optic crystal substrate12. That is, the electro-optic crystal substrate 12 may for example be asubstrate of a z-cut. A thickness T12 of the electro-optic crystalsubstrate 12 may for example be, but not particularly limited to, atleast 0.1 μm and 10 μm at most.

Here, the smaller a thickness T12 of the electro-optic crystal substrate12 is, the more likely it is that a propagation loss of light increasesand a coupling loss with an optical fiber increases. Due to this, thethickness T12 of the electro-optic crystal substrate 12 is preferably atleast 0.3 μm, and more preferably at least 0.45 μm. On the other hand,the larger the thickness T12 of the electro-optic crystal substrate 12is, the more difficult it becomes to realize a high-speed operation anda driving voltage reduction of the electro-optic element. From theseviewpoints, the thickness T12 of the electro-optic crystal substrate 12is preferably 5 μm at most, and more preferably 2.8 μm at most.

A material constituting the electro-optic crystal substrate 12 may be,but not particularly limited to, one of lithium niobate, lithiumtantalate, potassium titanyl phosphate, potassium lithium niobate,potassium niobate, potassium tantalate niobate, and a solid solution oflithium niobate and lithium tantalate. The electro-optic crystalsubstrate 12 may have an electro-optical effect of changing anotheroptical constant in addition to or as an alternative of the refractiveindex.

The low-refractive-index layer 14 is in contact with the electro-opticcrystal substrate 12 under the electro-optic crystal substrate 12. Thelow-refractive-index layer 14 has a refractive index that is lower thanthat of the electro-optic crystal substrate 12. Due to this, lightpropagating through the electro-optic crystal substrate 12 is highlylikely to be fully reflected at an interface F1 between theelectro-optic crystal substrate 12 and the low-refractive-index layer14, by which leakage of the light from the electro-optic crystalsubstrate 12 can be reduced. A material constituting thelow-refractive-index layer 14 may be, but not particularly limited to,at least one substance selected from a group consisting of siliconoxide, tantalum oxide, aluminum oxide, magnesium fluoride, and calciumfluoride. A thickness T14 of the low-refractive-index layer 14 may forexample be, but not particularly limited to, at least 0.1 μm and 10 μmat most.

The smaller thickness T14 of the low-refractive-index layer 14 is, themore difficult it becomes to satisfy a rate matching condition of theelectro-optic element, by which the high-speed operation of theelectro-optic element becomes difficult. From this viewpoint, it ispreferable that the thickness T14 of the low-refractive-index layer 14is at least 0.65 μm, and more preferably 0.7 μm. Further, the larger thethickness T14 of the low-refractive-index layer 14 is, the more likelyit is that a crack is created in the electro-optic crystal substrate 12and in the support substrate 18 caused by a thermal stress due to athermal expansion coefficient difference. Especially in the compositesubstrate 10 that uses direct bonding, due to absence of a bonding layerwith a low elastic modulus and constituted of resin, the thermal stresscaused by the thermal expansion coefficient difference is likely toincrease easily. Due to this, the thickness T14 of thelow-refractive-index layer 14 is preferably 9 μm at most, and morepreferably 7 μm at most.

In addition, since the refractive index is proportional to a square rootof a dielectric constant, a dielectric constant of thelow-refractive-index layer 14 is lower than a dielectric constant of theelectro-optic crystal substrate 12. As such, when the compositesubstrate 10 includes the low-refractive-index layer 14, it becomeseasier to satisfy the rate matching condition and adjust acharacteristic impedance in the electro-optic elements manufactured fromthe composite substrate 10. Further, since a floating capacitance anddielectric loss can be reduced, the high-speed operation and voltagereduction of the electro-optic element are realized.

The bonding layer 16 is located between the low-refractive-index layer14 and the support substrate 18. A thickness T16 of the bonding layer 16may be, but not particularly limited to, at least 0.01 μm and 1 μm atmost. Although details will be described later, in the manufacturingmethod of the composite substrate 10, the low-refractive-index layer 14and the bonding layer 16 are formed on the electro-optic crystalsubstrate 12, and thereafter the support substrate 18 is bonded to thebonding layer 16 by direct bonding. The bonding layer 16 is a coatingprovided for this direct bonding, and can be configured of a materialsuitable for the direct bonding. In regard to this point, the materialwhich constitutes the bonding layer 16 may be at least one substanceselected from a group consisting of tantalum oxide, niobium oxide,silicon, aluminum oxide, and titanium oxide. Alternatively, the materialwhich constitutes the bonding layer 16 may be at least one of gold,silver, copper, aluminum, platinum, and an alloy containing at least twoof the aforementioned metal elements.

The support substrate 18 is a lowermost layer of the composite substrate10, and its lower surface 18 b is exposed to outside. The supportsubstrate 18 is disposed to increase a strength of the compositesubstrate 10, by which the thickness of the electro-optic crystalsubstrate 12 can be decreased. A thickness T18 of the support substrate18 may for example be, but not particularly limited to, at least 100 μmand 1000 μm at most. The support substrate 18 may be, but notparticularly limited to, a substrate constituted of lithium niobate,lithium tantalate, silicon, glass, sialon, mullite, aluminum nitride,silicon nitride, magnesium oxide, sapphire, quartz, crystal, galliumnitride, silicon carbide, or gallium oxide. In order to mitigate thermaldeformation (especially warping) of the composite substrate 10, thecloser a linear expansion coefficient of the support substrate 18 is toa linear expansion coefficient of the electro-optic crystal substrate12, the more preferable. In regard to this feature, a materialconstituting the support substrate 18 may be the same as the materialconstituting the electro-optic crystal substrate 12.

In the composite substrate 10 of the present embodiment, the larger athickness T18 of the support substrate 18 is, the higher a mechanicalstrength of the composite substrate 10 (that is, a mechanical strengthof the electro-optic element) can be. On the other hand, the larger thethickness T18 of the support substrate 18 is, the more likely it is thatthe electromagnetic waves resonate within the composite substrate 10when the electro-optic element is used in a radio frequency band (forexample, 10 GHz or higher). When such a resonance occurs, a normaloperation of the electro-optic element is thereby obstructed, such as byan unintended ripple (fluctuation) occurring in an output signal of theelectro-optic element.

To address the above problem, in the composite substrate 10 of thepresent embodiment, an interface F2 between the low-refractive-indexlayer 14 and the bonding layer 16 is configured as an interface with alarger roughness than the interface F1 between the electro-optic crystalsubstrate 12 and the low-refractive-index layer 14. According to such aconfiguration, the electromagnetic waves propagating within thecomposite substrate 10 in the thickness direction are refracted orreflected in various ways on the rough interface F2, which createsnumerous variations in paths along which the electromagnetic wavespropagate. Due to this, the electromagnetic waves propagating within thecomposite substrate 10 can be suppressed from overlapping each other inthe same phase in the thickness direction.

Especially, the interface F2 between the low-refractive-index layer 14and the bonding layer 16 is located closer to the electro-optic crystalsubstrate 12 than for example an interface F3 between the bonding layer16 and the support substrate 18 is to the electro-optic crystalsubstrate 12. The closer the rough interface F2 is located with respectto the electro-optic crystal substrate 12, the more different directionsthe electromagnetic waves can be refracted or reflected in in a vicinityof the electro-optic crystal substrate 12. Due to this, the variationsof the propagation path of the electromagnetic waves can further beincreased, and a loss caused by the ripples, for example, can besignificantly reduced by effective reduction of the substrate resonance.Further, the composite substrate 10 of the present embodiment has amulti-layer structure and multiple interfaces F1, F2, F3 havingdifferent dielectric constants are present, resulting in the structurewhich allows for multipath reflections of electromagnetic waves. Thus,even when an arithmetic roughness average (Ra) of the rough interface F2is 10 nm at most, the substrate resonance can sufficiently be reduced.

In the composite substrate 10 of the present embodiment, the roughnessof the interface F2 between the low-refractive-index layer 14 and thebonding layer 16 may be at least three times a roughness of theinterface F1 between the electro-optic crystal substrate 12 and thelow-refractive-index layer 14. Alternatively, the roughness of theinterface F2 may be at least five times, or ten times the roughness ofthe interface F1. The larger a roughness difference between these twointerfaces F1, F2 is, the greater the effect of the art disclosed hereincan sufficiently be.

In the composite substrate 10 of the present embodiment, the arithmeticroughness average (Ra) of the interface F1 between the electro-opticcrystal substrate 12 and the low-refractive-index layer 14 may be in arange from 0.03 nm to 0.5 nm. Further, an arithmetic roughness average(Ra) of the interface F2 between the low-refractive-index layer 14 andthe bonding layer 16 may be in a range from 0.5 nm to 500 nm. When thecomposite substrate 10 satisfies these numerical requirements, thecomposite substrate 10 achieving the effect of the art disclosed hereincan be manufactured with a relatively simple procedure.

From a viewpoint of further reduction of the substrate resonance, thearithmetic roughness average (Ra) of the interface F2 is preferably atleast 0.6 nm, and more preferably at least 1.5 nm. On the other hand,when the arithmetic roughness average (Ra) of the interface F2 isincreased, a film quality of the bonding layer 16 could be degraded,which may result in a reduced bonding strength. Due to this, thearithmetic roughness average (Ra) of the interface F2 is more preferably10 nm at most, and yet more preferably 7 nm at most.

In the composite substrate 10 of the present embodiment, the arithmeticroughness average (Ra) of the interface F2 between thelow-refractive-index layer 14 and the bonding layer 16 may be at leastone thousandth ( 1/1000) of the thickness T14 of thelow-refractive-index layer 14. In addition thereto or as an alternativethereof, the arithmetic roughness average (Ra) of the interface F2between the low-refractive-index layer 14 and the bonding layer 16 maybe at least 0.5 nm, and the thickness of the low-refractive-index layer14 may be at least 0.5 μm. When the composite substrate 10 satisfiesthese numerical requirements, the composite substrate 10 achieving theeffect of the art disclosed herein can be manufactured with a relativelysimple procedure.

As an example, a first sample was fabricated by configuring theelectro-optic crystal substrate 12 as a lithium niobate substrate andthe thickness T12 thereof as 1.5 μm. In this sample, thelow-refractive-index layer 14 was constituted of silicon oxide, itsthickness T14 was set to 0.7 μm, the bonding layer 16 was constituted oftantalum oxide, and its thickness T16 was set to 0.05 nm. The supportsubstrate 18 was a lithium niobate substrate, having the thickness T18of 1000 μm. The arithmetic roughness average (Ra) of the interface F1between the electro-optic crystal substrate 12 and thelow-refractive-index layer 14 was 0.2 nm, and the arithmetic roughnessaverage (Ra) of the interface F2 between the low-refractive-index layer14 and the bonding layer 16 was 0.7 nm. An optical modulator wasmanufactured using the first sample and electric signals in a range of 0to 110 GHz were applied to the electro-optic crystal substrate 12. Noripples were detected in output signals of the optical modulator.

As another example, a second sample in which the thickness T14 of thelow-refractive-index layer 14 in the aforementioned first sample waschanged to 2.5 μm was fabricated. In this sample, the arithmeticroughness average (Ra) of the interface F1 between the electro-opticcrystal substrate 12 and the low-refractive-index layer 14 was 0.2 nm,and the arithmetic roughness average (Ra) of the interface F2 betweenthe low-refractive-index layer 14 and the bonding layer 16 was 2.5 nm.An optical modulator was manufactured using the second sample andelectric signals in the range of 0 to 110 GHz were applied to theelectro-optic crystal substrate 12. No ripples were detected in outputsignals of the optical modulator.

Hereinbelow, a method of manufacturing the composite substrate 10 willbe described with reference to FIGS. 3 to 7. Firstly, as shown in FIG.3, the electro-optic crystal substrate 12 is prepared and thelow-refractive-index layer 14 is formed on the lower surface 12 b of theelectro-optic crystal substrate 12. In doing so, a roughness of a lowersurface 14 b of the low-refractive-index layer 14 is increased to belarger than a roughness of the lower surface 12 b of the electro-opticcrystal substrate 12. As a specific example, at the stage when theelectro-optic crystal substrate 12 is prepared, the arithmetic roughnessaverage (Ra) of the lower surface 12 b of the electro-optic crystalsubstrate 12 may preferably be in a range from 0.03 nm to 0.5 nm.Further, the arithmetic roughness average (Ra) of the lower surface 14 bof the low-refractive-index layer 14 may preferably be in a range from0.5 nm to 500 nm.

Formation of the low-refractive-index layer 14 can be performed bysputter deposition, but not particularly limited thereto. When thelow-refractive-index layer 14 is formed by the sputter deposition, theroughness of the lower surface 14 b of the low-refractive-index layer 14naturally becomes larger than the roughness of the lower surface 12 b ofthe electro-optic crystal substrate 12. Especially when thelow-refractive-index layer 14 is constituted of silicon oxide, thistendency is more prominently exhibited. As such, when thelow-refractive-index layer 14 is formed by the sputter deposition, aprocess of roughening the lower surface 14 b of the low-refractive-indexlayer 14 can be either omitted or simplified. However, a method offorming the low-refractive-index layer 14 is not limited to the sputterdeposition, and it may for example be various vapor depositions such asa physical vapor deposition (PVD) and a chemical vapor deposition (CVD),or thermal oxidization. Further, after the formation of thelow-refractive-index layer 14, a process of roughening the lower surface14 b of the low-refractive-index layer 14 (such as lapping, sand blast,and etching) may be performed as needed.

The electro-optic crystal substrate 12 may for example be a substrate ofthe x-cut or the y-cut (having the c-axis parallel to the substrate), ormay be a substrate of a z-cut (having the c-axis vertical to thesubstrate). Further, if a reverse polarized portion is to be formed, theelectro-optic crystal substrate 12 may be an offset substrate having thec-axis forming an angle less than or equal to 10 degree with ahorizontal plane of the substrate.

Next, as shown in FIG. 4, the bonding layer 16 is formed on the lowersurface 14 b of the low-refractive-index layer 14. The bonding layer 16can be formed by sputter deposition, similar to the low-refractive-indexlayer 14. However, a step of forming the low-refractive-index layer 14is not limited to the sputter deposition, and may for example be vapordeposition (physical or chemical vapor deposition). Next, as shown inFIG. 5, a lower surface 16 b of the bonding layer 16 is smoothed by forexample polishing. Since the bonding layer 16 is formed on the lowersurface 14 b of the low-refractive-index layer 14 having the largeroughness, a roughness of the lower surface 16 b of the bonding layer 16may also relatively be larger. Due to this, prior to a step of bondingthe support substrate 18 to be described later, the lower surface 16 bof the bonding layer 16 may be smoothed as needed.

Next, as shown in FIG. 6, the support substrate 18 is prepared and thesupport substrate 18 is bonded to the lower surface 16 b of the bondinglayer 16. This bonding of the support substrate 18 may be performed bydirect bonding, but not particularly limited thereto. Finally, as shownin FIG. 7, the electro-optic crystal substrate 12 is processed to thedesired thickness by polishing the upper surface 12 a of theelectro-optic crystal substrate 12.

As shown in FIG. 8, electrodes 32, 34 may further be disposed on thecomposite substrate 10. These electrodes 32, 34 are disposed on theupper surface 12 a of the electro-optic crystal substrate 12 forapplying an electric signal to the electro-optic crystal substrate 12. Amaterial constituting the electrodes 32, 34 only needs to be an electricconductor, and may for example be metal such as gold, silver, copper,aluminum, and platinum. The electrodes 32, 44 may each include a layerof titanium (Ti), chrome (Cr), nickel (Ni), or platinum as a base layer(lowermost layer) to be in contact with the electro-optic crystalsubstrate 12 for preventing exfoliation and migration of the electrodes32, 34. Numbers, positions, and shapes of the electrodes 32, 34 are notparticularly limited. As for the numbers of the electrodes 32, 34, theymay suitably be determined in accordance with the number of theelectro-optical elements manufactured from the composite substrate 10and numbers of the electrodes 32, 34 which those electro-optic elementsrequire. When the electrodes 32, 34 are predisposed on the compositesubstrate 10, a manufacturer of the electro-optic elements can easilymanufacture the electro-optic elements from the composite substrate 10.

In addition thereto or as an alternative thereof, an optical waveguideregion 36 may be disposed in the electro-optic crystal substrate 12 bydoping impurities. In the electro-optic crystal substrate 12, itsrefractive index can selectively (that is, locally) be increased bydoping specific impurities such as titanium or zinc, and the opticalwaveguide region 36 can thereby be formed. The number, a position, and ashape of the optical waveguide region 36 are also not particularlylimited. For example, the number of the optical waveguide region 36 maysuitably be determined in accordance with the number of theelectro-optical elements manufactured from the composite substrate 10and the number of the optical waveguide region 36 which thoseelectro-optic elements require. When the optical waveguide region 36 ispredisposed on the composite substrate 10, a manufacturer of theelectro-optic elements can easily manufacture the electro-optic elementsfrom the composite substrate 10.

As shown in FIG. 9, a ridge portion 13 may be formed on the uppersurface 12 a of the electro-optic crystal substrate 12. The ridgeportion 13 is a protrusion that extends long along the upper surface 12a. The ridge portion 13 configures a ridge type optical waveguide in theelectro-optical elements manufactured from the composite substrate 10.When the ridge portion 13 is preformed on the composite substrate 10,manufacture of the electro-optic elements that require the ridge typeoptical waveguide can easily be performed. A width W of the ridgeportion 13 may be, but not particularly limited to, at least 1 μm and 10μm at most. A height TR of the ridge portion 13 may be, but similarlynot particularly limited to, at least 10 percent and 95 percent at mostof the thickness T12 of the electro-optic crystal substrate 12. Thenumber, a position, and a shape of the ridge portion 13 are also notparticularly limited. Although this is merely an example, when thecomposite substrate 10 is used for manufacturing a Mach-Zehnderelectro-optic modulator, two ridge portions 13 which at least partiallyextend parallel to each other may be formed.

As shown in FIG. 10, a first electrode 42 and a second electrode 44 mayfurther be disposed on the composite substrate 10 having the ridgeportion 13. Here, if the c-axis of the electro-optic crystal substrate12 is parallel to the electro-optic crystal substrate 12, the firstelectrode 42 may be disposed on one side surface 13 a of the ridgeportion 13. Further, the second electrode 44 may be disposed on anotherside surface 13 b of the ridge portion 13 and oppose the first electrode42 across the ridge portion 13. According to such a configuration, thefirst electrode 42 and the second electrode 44 can apply an electricfield to the ridge portion 13 being the optical waveguide in theelectro-optic element in a direction parallel to the c-axis.

As shown in FIG. 11, the c-axis of the electro-optic crystal substrate12 may be perpendicular to the electro-optic crystal substrate 12. Inthis case as well, the ridge portion 13 may be formed on the uppersurface 12 a of the electro-optic crystal substrate 12. Further, a firstelectrode 52 and a second electrode 54 may further be disposed on theupper surface 12 a of the electro-optic crystal substrate 12. However,the first electrode 52 is preferably disposed on a top surface 13 c ofthe ridge portion 13 and the second electrode 54 is preferably disposedin a region within the upper surface 12 a of the electro-optic crystalsubstrate 12 excluding the ridge portion 13. According to such aconfiguration, the first electrode 52 and the second electrode 54 canapply an electric field to the ridge portion 13 being the opticalwaveguide in the electro-optic element in a direction parallel to thec-axis.

(Second Embodiment) A composite substrate 10 a of a second embodimentwill be described with reference to FIGS. 12 and 13. As shown in FIG.12, the composite substrate 10 a of the second embodiment furtherincludes an intermediate layer 20 located between thelow-refractive-index layer 14 and the bonding layer 16, and differs fromthe composite substrate 10 of the first embodiment in this regard.Further, an interface F5 between the intermediate layer 20 and thebonding layer 16 is configured, instead of the interface F2 between thelow-refractive-index layer 14 and the bonding layer 16, as an interfacehaving a larger roughness than the interface F1 between theelectro-optic crystal substrate 12 and the low-refractive-index layer14. With such a configuration as well, the resonance of theelectromagnetic waves within the composite substrate 10 a can be reducedby presence of the rough interface F5 in the composite substrate 10 a.Instead of or in addition to the interface F5 between the intermediatelayer 20 and the bonding layer 16, an interface F4 between thelow-refractive-index layer 14 and the intermediate layer 20 may be aninterface having a larger roughness than the interface F1 between theelectro-optic crystal substrate 12 and the low-refractive-index layer14. With presence of multiple rough interfaces, the electromagneticwaves propagating inside the composite substrate 10 a along thethickness direction are even less likely to overlap each other in thesame phase than in a case with only one rough interface, and theresonance of the electromagnetic waves can further be reduced.

As shown in FIG. 13, as for the composite substrate 10 a of the presentembodiment as well, it can be manufactured by bonding the electro-opticcrystal substrate 12 to the support substrate 18. In this case, theintermediate layer 20 may be preformed on the electro-optic crystalsubstrate 12 between the low-refractive-index layer 14 and the bondinglayer 16. Further, when the intermediate layer 20 is to be formed, aroughness of a lower surface 20 b of the intermediate layer 20 may beincreased. Due to this, the interface F5 between the intermediate layer20 and the bonding layer 16 in the manufactured composite substrate 10can be configured as the interface having the larger roughness than theinterface F1 between the electro-optic crystal substrate 12 and thelow-refractive-index layer 14.

A material constituting the intermediate layer 20 may be a materialwhich may be employed in the low-refractive-index layer 14 or in thebonding layer 16. Further, it may be a material different frommaterial(s) actually employed in the low-refractive-index layer 14 andthe bonding layer 16. However, since the intermediate layer 20 islocated between the electro-optic crystal substrate 12 and the roughinterface F5, employment of electric conductors such as metal as thematerial constituting the intermediate layer 20 is preferably avoided sothat the electromagnetic waves are not intercepted by the intermediatelayer 20.

(Third Embodiment) A composite substrate 10 b of a third embodiment willbe described with reference to FIGS. 14 and 15. As shown in FIG. 14, inthe composite substrate 10 b of the third embodiment, the interface F3between the bonding layer 16 and the support substrate 18 is configuredas an interface having a larger roughness than the interface F1 betweenthe electro-optic crystal substrate 12 and the low-refractive-indexlayer 14. With such a configuration as well, the resonance of theelectromagnetic waves within the composite substrate 10 b can be reducedby presence of the rough interface F3 in the composite substrate 10 b.In addition to the interface F3 between the bonding layer 16 and thesupport substrate 18, another interface F2 may further be configured asan interface having a larger roughness than the interface F1 between theelectro-optic crystal substrate 12 and the low-refractive-index layer14.

As shown in FIG. 15, as for the composite substrate 10 b of the presentembodiment as well, it can be manufactured by bonding the electro-opticcrystal substrate 12 to the support substrate 18. However, it ispreferable to first roughen an upper surface 18 a of the supportsubstrate 18 and then form a bonding layer 16′ on this upper surface 18a in advance. By doing so, the interface F3 between the bonding layer 16and the support substrate 18 in the manufactured composite substrate 10b can be configured as the interface having the larger roughness thanthe interface F1 between the electro-optic crystal substrate 12 and thelow-refractive-index layer 14. Further, due to the bonding layers 16,16′ being formed respectively on the electro-optic crystal substrate 12and on the support substrate 18, the substrates 12, 18 can easily bebonded.

(Fourth Embodiment) A composite substrate 10 c of a fourth embodimentwill be described with reference to FIGS. 16 and 17. As shown in FIG.16, the composite substrate 10 c of the fourth embodiment furtherincludes an intermediate layer 22 located between the bonding layer 16and the support substrate 18, and differs from the composite substrate10 b of the third embodiment in this regard. Further, an interface F6between the intermediate layer 22 and the bonding layer 16 isconfigured, instead of the interface F3 between the bonding layer 16 andthe support substrate 18, as an interface having a larger roughness thanthe interface F1 between the electro-optic crystal substrate 12 and thelow-refractive-index layer 14. With such a configuration as well, theresonance of the electromagnetic waves within the composite substrate 10c can be reduced by presence of the rough interface F6 in the compositesubstrate 10 c. In addition to the interface F6 between the intermediatelayer 22 and the bonding layer 16, other interfaces F2, F7 may furtherbe configured as interfaces having a larger roughness than the interfaceF1 between the electro-optic crystal substrate 12 and thelow-refractive-index layer 14.

As shown in FIG. 17, the composite substrate 10 c of the presentembodiment as well can be manufactured by bonding the electro-opticcrystal substrate 12 to the support substrate 18. In this case, theintermediate layer 22 and the bonding layer 16′ may be preformed on thesupport substrate 18. Further, when the intermediate layer 22 is formed,a roughness of an upper surface 22 a of the intermediate layer 22 may beincreased. Due to this, the interface F6 between the bonding layer 16and the intermediate layer 22 in the manufactured composite substrate 10c can be configured as the interface having the larger roughness thanthe interface F1 between the electro-optic crystal substrate 12 and thelow-refractive-index layer 14.

In the composite substrates 10 and 10 a to 10 c of the first to fourthembodiments, the bonding layer 16 and the intermediate layers 20, 22 maybe constituted of electric conductors such as metal. However, when sucha conductive layer is present, the electromagnetic waves propagatingthrough the composite substrates 10 and 10 a to 10 c are interceptedwithout passing through the conductive layer, thus they propagateprimarily in an area between the electro-optic crystal substrate 12 andthe conductive layer. Due to this, the rough interface is preferablylocated in the area between the electro-optic crystal substrate 12 andthe conductive layer where the electromagnetic waves primarilypropagate.

REFERENCE SIGNS LIST

-   10: Composite Substrate-   12: Electro-Optic Crystal Substrate-   13: Ridge Portion-   14: Low-Refractive-Index Layer-   16, 16′: Bonding Layer-   18: Support Layer-   20, 22: Intermediate Layer-   32, 34, 42, 44, 52, 54: Electrode-   36: Optical Waveguide Region-   F1-F7: Interface

1. A composite substrate for an electro-optic element, the compositesubstrate comprising: an electro-optic crystal substrate having anelectro-optic effect; a low-refractive-index layer being in contact withthe electro-optic crystal substrate and having a lower refractive indexthan the electro-optical crystal substrate; and a support substratebonded to the low-refractive-index layer at least via a bonding layer,wherein a plurality of interfaces located between thelow-refractive-index layer and the support substrate includes at leastone rough interface having a roughness that is larger than a roughnessof an interface between the electro-optic crystal substrate and thelow-refractive-index layer, and an arithmetic roughness average (Ra) ofthe at least one rough interface is in a range from 0.5 nm to 10 nm. 2.(canceled)
 3. The composite substrate according to claim 1, wherein athickness of the low-refractive-index layer is in a range from 0.1 μm to10 μm.
 4. The composite substrate according to claim 1, wherein athickness of the electro-optic crystal substrate is in a range from 0.1μm to 10 μm.
 5. The composite substrate according to claim 1, whereinthe roughness of the at least one rough interface is at least threetimes the roughness of the interface between the electro-optic crystalsubstrate and the low-refractive-index layer.
 6. The composite substrateaccording to claim 1, wherein the roughness of the at least one roughinterface is at least five times the roughness of the interface betweenthe electro-optic crystal substrate and the low-refractive-index layer.7. The composite substrate according to claim 1, wherein an arithmeticroughness average (Ra) of the interface between the electro-opticcrystal substrate and the low-refractive-index layer is in a range from0.03 nm to 0.5 nm, and an arithmetic roughness average (Ra) of the atleast one rough interface is in a range from 0.5 nm to 500 nm.
 8. Thecomposite substrate according to claim 1, wherein the at least one roughinterface is an interface between the low-refractive-index layer and thebonding layer.
 9. The composite substrate according to claim 8, whereinan arithmetic roughness average (Ra) of the interface between thelow-refractive-index layer and the bonding layer is at least onethousandth of a thickness of the low-refractive-index layer.
 10. Thecomposite substrate according to claim 8, wherein an (the) arithmeticroughness average (Ra) of the interface between the low-refractive-indexlayer and the bonding layer is at least 0.5 nm, and the thickness of thelow-refractive-index layer is at least 0.5 μm.
 11. The compositesubstrate according to claim 1, wherein the at least one rough interfaceis an interface between the bonding layer and the support substrate. 12.The composite substrate according to claim 1, further comprising anintermediate layer located between the low-refractive-index layer andthe bonding layer, wherein the at least one rough interface is aninterface between the intermediate layer and the bonding layer.
 13. Thecomposite substrate according to claim 1, further comprising anintermediate layer located between the bonding layer and the supportlayer, wherein the at least one rough interface is an interface betweenthe intermediate layer and the support layer.
 14. The compositesubstrate according to claim 1, further comprising a conductive layerconstituted of an electric conductor, wherein the at least one roughinterface includes one or more interfaces located between theelectro-optic crystal substrate and the conductive layer.
 15. Thecomposite substrate according to claim 14, wherein the conductive layeris at least a part of either the bonding layer or the intermediatelayer.
 16. The composite substrate according to claim 1, wherein theelectro-optic crystal substrate is a substrate of lithium niobate,lithium tantalate, potassium titanyl phosphate, potassium lithiumniobate, potassium niobate, potassium tantalate niobate, or a solidsolution of lithium niobate and lithium tantalate.
 17. The compositesubstrate according to claim 1, wherein the low-refractive-index layeris constituted of at least one substance selected from a groupconsisting of silicon oxide, tantalum oxide, aluminum oxide, magnesiumfluoride, and calcium fluoride.
 18. The composite substrate according toclaim 1, wherein the bonding layer is constituted of at least onesubstance selected from a group consisting of tantalum oxide, niobiumoxide, silicon, aluminum oxide, titanium oxide, gold, silver, copper,aluminum, platinum, and an alloy containing at least two of theaforementioned metal elements.
 19. The composite substrate according toclaim 1, wherein the support layer is a substrate constituted of lithiumniobate, lithium tantalate, silicon, glass, sialon, mullite, aluminumnitride, silicon nitride, magnesium oxide, sapphire, quartz, crystal,gallium nitride, silicon carbide, or gallium oxide.
 20. A method ofmanufacturing a composite substrate for an electro-optic element,comprising: forming a low-refractive-index layer on a surface of anelectro-optic crystal substrate having an electro-optic effect, thelow-refractive-index layer having a lower refractive index than theelectro-optic crystal substrate; forming a bonding layer on a surface ofthe low-refractive-index layer formed on the electro-optic crystalsubstrate; and bonding a support substrate on a surface of the bondinglayer formed on the low-refractive-index layer, wherein a roughness ofthe surface of the low-refractive-index layer before the forming of thebonding layer is larger than a roughness of the surface of theelectro-optic crystal substrate before the forming of thelow-refractive-index layer, and an arithmetic roughness average (Ra) ofthe surface of the low-refractive-index layer before the forming of thebonding layer is in a range from 0.5 nm to 10 nm.
 21. (canceled)
 22. Themethod according to claim 20, further comprising smoothing the surfaceof the bonding layer between the forming of the bonding layer and thebonding of the support substrate.
 23. The method according to claim 20,wherein the forming of the low-refractive-index layer comprises formingthe low-refractive-index layer by sputter deposition.
 24. The methodaccording to claim 20, further comprising forming a bonding layer on asurface of the support substrate before the bonding of the supportsubstrate.